Nothing will change.
1 - mining will continue - miners will be payed throught transaction fees
2 - There is nothing like "last bitcoin" its just slogan for not educated people - each 4 years mining reward from distribution pool is decrised by half. That means that in next 100+ years reward will be decrised to less than 1 sat - what means that it wont be payed. Total amount of bitcoins will be 21 mil than. But bitcoin is open sours code with proof of work (miners decides about code improvement). I'm sure that when peyment will be lesser than 1 sat easiest way to still get peyment will be changing the definition of satoshi. From 1/100 mln btc to 1/1bil btc - current 1 sat wil be 10 sat 1 btc will remain 1 btc so it wont change price. That will give another 4 years of mining with payment from distribution pool - which miner wont agree?
(i think they wont even bother about it - less than 1 sat per block...).
3- it wont affect price. Few years before that mining reward from distribution pool will be unnoticable for price (close to 1 sat per block is 52 000 sat per year which is 0.0005 btc per year for all miners - in last year of payment form distribution pool). Amount of lost bitcoins (wrong transfers, lost keys) each year will soon overlap distribution so situation with decrising amount of bitcoin each year will soon appear or even it is now.
4- if reward from transaction wont pay miners than some miners will quit what will decrise dificulty for others - nothing will change, we will just waste less energy
5 - imagince antminers in next 100 years - i bet that 1 device will handle to compute all transactions - others will just work as dificulty increase - network wont suffer
6- i dont think that it is a topic to talk about at all- in next 100+ years technology will change that much, and code will be change that much that even if you will educte yoursef and prepear for it future will be totally different.
7- i dont think that in next 100 yers bitcoin will remain proof of work - it may become proof of something what is not invented yet - if it wont evolve, it will be doomed to extinction - like everything in nature/economy/etc.
8- price wont become stable - at liest becaouse of that- distribution is stable x/block which mean x bitcoin each 10 min. It is not a thing that is a reason for bitcoin to pump 10000% than dump 80% in one year.
9- bitcoin will be more stable when it will hit 1 000 bil or 10 000 bil marketcap - it will need much more money to move price. We need big players with huge capital for that. Imagine if bitcoin has marketcap of 100$ - even I would be able to pump it 10000% - even if there is a new supply 10 btc each block (all 16 mln bitcoins are worth 100$ so those 10 each block won't stop me). Things are changing with bigger marketcap.